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Find the median of the data:
83, 37, 70, 29, 45, 63, 41, 70, 34, 54
Numbers are 83, 37, 70, 29, 45, 63, 41, 70, 34, 54
Arranging the numbers in ascending order
29, 34, 37, 41, 45, 54, 63, 70, 70, 83
n = 10 (even)
133, 73, 89, 108, 94, 104, 94, 85, 100, 120
Numbers are 133, 73, 89, 108, 94, 104, 94, 85, 100, 120
73, 85, 89, 94, 94, 100, 104, 108, 120, 133
31, 38, 27, 28, 36, 25, 35, 40
Numbers are 31, 38, 27, 28, 36, 25, 35, 40
25, 27, 28, 31, 35, 36, 38, 40
n = 8 (even)
15, 6, 16, 8, 22, 21, 9, 18, 25
Numbers are 15, 6, 16, 8, 22, 21, 9, 18, 25
6, 8, 9, 15, 16, 21, 22, 25
n = 9 (odd)
= 5th value = 16
41, 43, 127, 99, 71, 92, 71, 58, 57
Numbers are 41, 43, 127, 99, 71, 92, 71, 58, 57
41, 43, 57, 58, 71, 71, 92, 99, 127
= 5th value = 71
25, 34, 31, 23, 22, 26, 35, 29, 20, 32
Numbers are 25, 34, 31, 23, 22, 26, 35, 29, 20, 32
20, 22, 23, 25, 26, 29, 31, 32, 34, 35
12, 17, 3, 14, 5, 8, 7, 15
Numbers are 12, 17, 3, 14, 5, 8, 7, 15
3, 5, 7, 8, 12, 14, 15, 17
92, 35, 67, 85, 72, 81, 56, 51, 42, 69
Numbers are 92, 35, 67, 85, 72, 81, 56, 51, 42, 69
35, 42, 51, 56, 67, 69, 72, 81, 85, 92
n = 10(even)
Numbers 50, 42, 35, 2x + 10, 2x – 8, 12, 11, 8 are written in descending order and their median is 25, find x.
Given the number of observation, n = 8
= 2x + 1
Given Median = 25
∴ 2x + 1 = 25
⇒ 2x = 24
⇒ x = 12
Find the median of the following observations: 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33. If 92 is replaced by 99 and 41 by 43 in the above data, find the new median?
Given the numbers are 46, 64, 87, 41, 58, 77, 35, 90, 55, 92, 33
33, 35, 41, 46, 55, 58, 64, 77, 87, 90, 92
n = 11 (odd)
= 6th value = 58
If 92 is replaced by 99 and 41 by 43
Then the new values are: 33, 35, 43, 46, 55, 58, 64, 77, 87, 90, 99
Find the median of the following data: 41, 43, 127, 99, 61, 92, 71, 58, 57. If 58 is replaced by 85, what will be the new median?
Given the numbers are 41, 43, 127, 99, 61, 92, 71, 58, 57
41, 43, 57, 58, 61, 71, 92, 99, 127
If 58 is replaced by 85
Then the new values be in order are: 41, 43, 57, 61, 71, 85, 92, 99, 127
The weights (in kg) of 15 students are: 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30. Find the median. If the weight 44 kg is replaced by 46 kg and 27 kg by 25 kg, find the new median.
Given the numbers are 31, 35, 27, 29, 32, 43, 37, 41, 34, 28, 36, 44, 45, 42, 30
27, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 44, 45.
n = 15 (odd)
= 8th value = 35 kg
If the weight 44 kg is replaced by 46 kg and 27 kg is replaced by 25 kg
Then the new values be in order are: 25, 28, 29, 30, 31, 32, 34, 35, 36, 37, 41, 42, 43, 45, 46
The following observation s have been arranged in ascending order. If the median of the data is 63, find the value of x: 29, 32, 48, 50, x, x + 2, 72, 78, 84, 95.
Total number of observation in the given data is 10 (even number). So median of this data will be mean of 10/2 i. e, 5th observation and 10/2 + 1 i. e, 6th observation. So,
⇒ 63 = x + 1
⇒ x = 62
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Chapter 24: Measures of Central Tendency Exercise...